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Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions

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arxiv 2211.14188 v1 pith:PIM2MIGE submitted 2022-11-25 math.FA math.PR

Esther Bou Dagher , Yaozhong Qiu , Boguslaw Zegarlinski , Mengchun Zhang This is my paper · ORCID
classification math.FAmath.PR
keywords inequalitiesspectralgroupsinfinitemeasuresnilpotentweakcarnot-caratheodory
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We develop a general framework for spectral gap inequalities for Gibbs measures on infinite dimensional spin spaces over nilpotent Lie groups in terms of weak U-bounds and weak single-site spectral gap inequalities. We then provide sufficient conditions on the local specification and give examples of measures constructed using the Kaplan norm and generalising a few results for the Carnot-Caratheodory distance on the Heisenberg group.

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  1. Optimal subelliptic super-Poincar\'e and isoperimetric inequalities on stratified Lie groups

    math.PR 2024-11 conditional novelty 7.0 of 10

    Exponential-power measures on stratified Lie groups, Grushin and Heisenberg-Greiner spaces satisfy q-super-Poincaré and isoperimetric inequalities with optimal exponent r=(α+1)p/(α+1+αp).

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